{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# hwB04 - ENEE 241 02 HOMEWORK ASSIGNMENT 4 Due Fri 02/08...

This preview shows pages 1–2. Sign up to view the full content.

ENEE 241 02* HOMEWORK ASSIGNMENT 4 Due Fri 02/08 Consider the discrete-time sinusoids x [ n ] = cos 3 πn 4 + 2 π 3 and y [ n ] = cos πn 5 + 2 π 3 (i) (4 pts.) What is the period N of x [ · ]? Use MATLAB to generate a discrete plot of the first four periods of x [ · ], (i.e., for n = 0 , . . . , 4 N - 1.) (ii) (4 pts.) How many different sinusoids of the form cos( ωn ) are periodic with the same fundamental period as x [ · ]? Determine the values of ω in [0 , 2 π ) that produce these sinusoids. (iii) (4 pts.) The sequence v [ · ] is formed by taking every second sample in y [ · ], i.e., v [ n ] = y [2 n ] Write an equation for v [ n ]. What is the period of v [ · ]? (iv) (4 pts.) Use reasoning (possibly aided by MATLAB) to determine whether x [ n ] + y [ n ] is periodic. If it is, what is its fundamental period? (v) (4 pts.) Is the function z [ n ] = x [ n ] 2 periodic? If it is, what is its fundamental period? Solved Examples S 4.1 . Find all frequencies ω in [0 , π ] for which the discrete-time sinusoid x [ n ] = cos ωn is periodic with fundamental period N = 16.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}